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On the Fourier extension of non-periodic functions

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If you have a question about this talk, please contact Carola-Bibiane Schoenlieb .

Fourier series exhibit rapid converge for (smooth and) periodic functions, but this is not the case for non-periodic functions. In this talk we analyze an interesting approach to eliminate the Gibbs phenomenon. Our approach leads to exponentially accurate Fourier series for non-periodic functions with pointwise convergence everywhere, including at the boundary. The analysis shows the path of generalization towards accurate Fourier series for multivariate functions defined on circles, triangles and higher-dimensional simplices.

This talk is part of the Applied and Computational Analysis Graduate Seminar series.

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